In [3]:
from pygadgetreader import *
import numpy as np
import pandas as pd

#import matplotlib
#matplotlib.use('Qt5Agg')
import matplotlib.pyplot as plt
import time
%matplotlib inline

import healpy as hp
from sklearn.neighbors import KDTree
In [4]:
# all scales are in Mpc/h
stackRadius = 2 
min_box = 0.0
max_box = 500.0
NSIDE = 32
min_edge = stackRadius*np.ones(3)
max_edge = max_box-stackRadius*np.ones(3)

1. Read halos

  • and extract coordinates. Here we may restrict it to certain halo size/mass range
In [5]:
dataDir = '/mnt/net/novo2/data/astro/nbody/millennium/'
haloFile = dataDir + 'halos.csv'
halos = pd.read_csv(haloFile,sep=',')
h_xyz0 = halos[['x','y','z']].values

2. Read Millenium and build tree

  • read the given block
  • determine bounding box
  • make kd-tree
  • collect neighbors of halos
  • calculate
In [6]:
def healPixStat(blockId):
    infile = '/mnt/local/data/astro/nbody/millennium/snapdir_063/snap_millennium_063.' + str(blockId)
    coordinates = readsnap(infile, 'pos', 'dm', single=1) ## single=1 makes it read only one block
    min_xyz = coordinates.min(axis=0)
    max_xyz = coordinates.max(axis=0)
    
    # generate kd-tree
    tree = KDTree(coordinates, leaf_size=2)  
    
    # select only halos in this block
    inidx = np.all((h_xyz0 >= min_xyz-stackRadius) & (h_xyz0 <= max_xyz+stackRadius) & (h_xyz0>min_edge) & (h_xyz0<max_edge) , axis=1)
    h_xyz = halos[inidx][['x','y','z']].values
    
    # get points around halos
    ind = tree.query_radius(h_xyz, r=stackRadius)
    
    # relative vectors
    neighvec= []
    for i in range(ind.shape[0]):
        xyz = h_xyz[i]
        neighvec.append(coordinates[ind[i]]-xyz)
    neighvec = np.vstack(np.array(neighvec))
    
    # healpix binned counts
    healIdx = hp.vec2pix(NSIDE, neighvec[:,0],neighvec[:,1],neighvec[:,2])
    healIdxList, healCounts = np.unique(healIdx, return_counts=True)
    
    return healCounts
    
In [155]:
def healPixStatHalfMassR(blockId):
    infile = '/mnt/local/data/astro/nbody/millennium/snapdir_063/snap_millennium_063.' + str(blockId)
    coordinates = readsnap(infile, 'pos', 'dm', single=1) ## single=1 makes it read only one block
    min_xyz = coordinates.min(axis=0)
    max_xyz = coordinates.max(axis=0)
    
    # generate kd-tree
    tree = KDTree(coordinates, leaf_size=2)  
    
    # select only halos in this block
    inidx = np.all((h_xyz0 >= min_xyz-stackRadius) & (h_xyz0 <= max_xyz+stackRadius) & (h_xyz0>min_edge) & (h_xyz0<max_edge) , axis=1)
    h_xyz = halos[inidx][['x','y','z']].values
    h_rad = 4*halos[inidx]['halfMassRadius'].values
    
    # get points around halos
    ind = tree.query_radius(h_xyz, r=h_rad)
    
    # relative vectors
    neighvec= []
    for i in range(ind.shape[0]):
        xyz = h_xyz[i]
        neighvec.append(coordinates[ind[i]]-xyz)
    neighvec = np.vstack(np.array(neighvec))
    
    # healpix binned counts
    healIdx = hp.vec2pix(NSIDE, neighvec[:,0],neighvec[:,1],neighvec[:,2])
    healIdxList, healCounts = np.unique(healIdx, return_counts=True)
    
    return healCounts
    
In [118]:
#for i in np.arange(30,dtype=int):
#for i in np.arange(30,dtype=int)+30:
#for i in np.arange(30,dtype=int)+60:
#for i in np.arange(30,dtype=int)+90:
#for i in np.arange(8,dtype=int)+120:
#for i in np.arange(32,dtype=int)+128:
for i in np.arange(352,dtype=int)+160:
    print(i,",",end='')
    start = time.time()
    if i == 0:
        stack = healPixStat(i)
    else:
        stack += healPixStat(i)
    end = time.time()
    print("%f s." %(end-start))
160 ,Returning DM    Positions
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In [119]:
stack.shape
Out[119]:
(12288,)
In [140]:
np.save(dataDir+'millHealpix2Mpc.npy',stack)
In [120]:
hp.mollview(stack, title="Mollview image RING")
hp.graticule()
0.0 180.0 -180.0 180.0
The interval between parallels is 30 deg -0.00'.
The interval between meridians is 30 deg -0.00'.
In [121]:
hp.mollview(hp.sphtfunc.smoothing(stack,0.1), title="Mollview image RING")
hp.graticule()
Sigma is 145.987664 arcmin (0.042466 rad) 
-> fwhm is 343.774677 arcmin
Sigma is 0.000000 arcmin (0.000000 rad) 
-> fwhm is 0.000000 arcmin
0.0 180.0 -180.0 180.0
The interval between parallels is 30 deg -0.00'.
The interval between meridians is 30 deg -0.00'.

Power spec

In [122]:
LMAX = 2*NSIDE
cl = hp.anafast(stack, lmax=LMAX)
ell = np.arange(len(cl))
In [123]:
alm = hp.sphtfunc.map2alm(stack, lmax=LMAX)
In [124]:
plt.figure(figsize=(10, 5))
plt.plot(ell, ell * (ell + 1) * cl)
plt.xlabel("$\ell$")
plt.ylabel("$\ell(\ell+1)C_{\ell}$")
plt.grid()
In [126]:
plt.figure(figsize=(10, 5))
k = 17
plt.plot(ell[:k], ell[:k] * (ell[:k] + 1) * cl[:k])
plt.xlabel("$\ell$")
plt.ylabel("$\ell(\ell+1)C_{\ell}$")
plt.grid()
In [127]:
LIM = 10000
plt.plot(alm.real,alm.imag,'.')
plt.xlim(-LIM,LIM)
plt.ylim(-LIM,LIM)
Out[127]:
(-10000, 10000)
In [135]:
plt.semilogy(np.abs(alm.real[:64]))
Out[135]:
[<matplotlib.lines.Line2D at 0x7f81c19faef0>]
In [132]:
plt.semilogy(np.abs(alm.imag[:100]))
Out[132]:
[<matplotlib.lines.Line2D at 0x7f81d80c1048>]

R= 0.5 Mpc/h

In [147]:
stackRadius = 0.5 

#for i in np.arange(32,dtype=int):
for i in np.arange(480,dtype=int)+32:
    print(i,",",end='')
    start = time.time()
    if i == 0:
        stack05 = healPixStat(i)
    else:
        stack05 += healPixStat(i)
    end = time.time()
    print("%f s." %(end-start))
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25.783873 s.
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41.113972 s.
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25.632344 s.
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24.290925 s.
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21.805262 s.
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25.683424 s.
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24.636920 s.
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25.832546 s.
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31.087046 s.
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26.303778 s.
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39.995721 s.
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33.648493 s.
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37.768825 s.
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39.095352 s.
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25.066275 s.
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36.431961 s.
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25.447943 s.
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508 ,Returning DM    Positions
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38.149780 s.
510 ,Returning DM    Positions
22.462818 s.
511 ,Returning DM    Positions
25.406737 s.
In [148]:
hp.mollview(stack05, title="Mollview image RING")
hp.graticule()
0.0 180.0 -180.0 180.0
The interval between parallels is 30 deg -0.00'.
The interval between meridians is 30 deg -0.00'.
In [149]:
LMAX = 2*NSIDE
cl05 = hp.anafast(stack05, lmax=LMAX)
ell05 = np.arange(len(cl05))
In [154]:
plt.figure(figsize=(10, 5))
plt.plot(ell05, ell05 * (ell05 + 1) * cl05)
plt.plot(ell, ell * (ell + 1) * cl/2000)
plt.xlabel("$\ell$")
plt.ylabel("$\ell(\ell+1)C_{\ell}$")
plt.title('R = 0.5 Mpc/h')
plt.grid()
#plt.xlim(0,17)

R= 4 x halfMassRadius

In [158]:
stackRadius = 0.5 

#for i in np.arange(5,dtype=int):
for i in np.arange(512,dtype=int):
    print(i,",",end='')
    start = time.time()
    if i == 0:
        stackR = healPixStatHalfMassR(i)
    else:
        stackR += healPixStatHalfMassR(i)
    end = time.time()
    print("%f s." %(end-start))
0 ,Returning DM    Positions
24.575250 s.
1 ,Returning DM    Positions
23.364319 s.
2 ,Returning DM    Positions
27.091832 s.
3 ,Returning DM    Positions
41.781519 s.
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39.324396 s.
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23.255033 s.
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26.803133 s.
7 ,Returning DM    Positions
187.491047 s.
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29.692605 s.
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43.679567 s.
10 ,Returning DM    Positions
26.063485 s.
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26.294942 s.
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30.931000 s.
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21.325915 s.
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27.236347 s.
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30.910559 s.
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27.051880 s.
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36.236677 s.
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37.931621 s.
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30.885365 s.
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37.113486 s.
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35.873267 s.
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29.914214 s.
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26.695277 s.
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30.631353 s.
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24.485146 s.
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32.843754 s.
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23.459400 s.
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22.493772 s.
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35.305626 s.
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26.766532 s.
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24.067510 s.
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22.675084 s.
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149.361643 s.
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25.909903 s.
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199 ,Returning DM    Positions
221.491353 s.
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28.572854 s.
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39.454130 s.
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27.547004 s.
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22.271254 s.
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220 ,Returning DM    Positions
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222 ,Returning DM    Positions
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35.667512 s.
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231 ,Returning DM    Positions
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30.478046 s.
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27.748078 s.
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55.034884 s.
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263 ,Returning DM    Positions
26.858021 s.
264 ,Returning DM    Positions
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22.771643 s.
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25.386533 s.
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269 ,Returning DM    Positions
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270 ,Returning DM    Positions
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33.763002 s.
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27.272540 s.
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30.785704 s.
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23.773792 s.
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48.254341 s.
279 ,Returning DM    Positions
316.176956 s.
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33.514816 s.
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22.171488 s.
283 ,Returning DM    Positions
73.418332 s.
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31.373158 s.
285 ,Returning DM    Positions
29.498157 s.
286 ,Returning DM    Positions
26.208930 s.
287 ,Returning DM    Positions
34.666309 s.
288 ,Returning DM    Positions
206.032375 s.
289 ,Returning DM    Positions
23.002695 s.
290 ,Returning DM    Positions
27.909436 s.
291 ,Returning DM    Positions
22.943056 s.
292 ,Returning DM    Positions
20.465738 s.
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22.692198 s.
294 ,Returning DM    Positions
35.717975 s.
295 ,Returning DM    Positions
33.996248 s.
296 ,Returning DM    Positions
28.469246 s.
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23.901075 s.
298 ,Returning DM    Positions
23.166638 s.
299 ,Returning DM    Positions
22.924115 s.
300 ,Returning DM    Positions
26.428412 s.
301 ,Returning DM    Positions
21.613242 s.
302 ,Returning DM    Positions
36.596315 s.
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23.771823 s.
304 ,Returning DM    Positions
33.350181 s.
305 ,Returning DM    Positions
27.001312 s.
306 ,Returning DM    Positions
39.864418 s.
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22.848017 s.
308 ,Returning DM    Positions
21.168089 s.
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40.674191 s.
310 ,Returning DM    Positions
23.071757 s.
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23.319320 s.
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20.835019 s.
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36.229717 s.
314 ,Returning DM    Positions
33.049161 s.
315 ,Returning DM    Positions
26.786599 s.
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30.654183 s.
318 ,Returning DM    Positions
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36.636168 s.
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31.809886 s.
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33.322869 s.
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26.006976 s.
323 ,Returning DM    Positions
23.468815 s.
324 ,Returning DM    Positions
229.984027 s.
325 ,Returning DM    Positions
41.038028 s.
326 ,Returning DM    Positions
24.127290 s.
327 ,Returning DM    Positions
145.922044 s.
328 ,Returning DM    Positions
40.646327 s.
329 ,Returning DM    Positions
47.194231 s.
330 ,Returning DM    Positions
570.882853 s.
331 ,Returning DM    Positions
21.435304 s.
332 ,Returning DM    Positions
21.326541 s.
333 ,Returning DM    Positions
26.414368 s.
334 ,Returning DM    Positions
56.995868 s.
335 ,Returning DM    Positions
28.150712 s.
336 ,Returning DM    Positions
24.039218 s.
337 ,Returning DM    Positions
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25.154035 s.
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29.292105 s.
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28.569669 s.
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36.914976 s.
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22.288218 s.
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21.803264 s.
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21.774840 s.
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30.844080 s.
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21.505363 s.
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36.070710 s.
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22.395653 s.
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27.906052 s.
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67.733488 s.
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22.617105 s.
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42.594370 s.
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29.905415 s.
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29.033982 s.
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34.716625 s.
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30.334727 s.
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25.966159 s.
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40.536067 s.
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40.494021 s.
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24.764166 s.
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21.914904 s.
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26.683221 s.
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23.850124 s.
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38.025230 s.
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23.363063 s.
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24.091832 s.
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20.335750 s.
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27.254616 s.
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23.144879 s.
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446 ,Returning DM    Positions
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31.449643 s.
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486 ,Returning DM    Positions
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26.408525 s.
507 ,Returning DM    Positions
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510 ,Returning DM    Positions
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511 ,Returning DM    Positions
23.411104 s.
In [159]:
hp.mollview(stackR, title="Mollview image RING")
hp.graticule()
0.0 180.0 -180.0 180.0
The interval between parallels is 30 deg -0.00'.
The interval between meridians is 30 deg -0.00'.
In [166]:
hp.mollview(hp.sphtfunc.smoothing(stackR,0.3), title="Mollview image RING")
hp.graticule()
Sigma is 437.962991 arcmin (0.127398 rad) 
-> fwhm is 1031.324031 arcmin
Sigma is 0.000000 arcmin (0.000000 rad) 
-> fwhm is 0.000000 arcmin
0.0 180.0 -180.0 180.0
The interval between parallels is 30 deg -0.00'.
The interval between meridians is 30 deg -0.00'.
In [162]:
LMAX = 2*NSIDE
clR = hp.anafast(stackR, lmax=LMAX)
ellR = np.arange(len(clR))
In [169]:
plt.figure(figsize=(10, 5))
plt.plot(ellR, ellR * (ellR + 1) * clR)
#plt.semilogy(ellR, ellR * (ellR + 1) * clR)
#plt.plot(ell, ell * (ell + 1) * cl/2000)
plt.xlabel("$\ell$")
plt.ylabel("$\ell(\ell+1)C_{\ell}$")
plt.title('R = 4 x halfMassRadius')
plt.grid()
#plt.xlim(0,17)
In [176]:
plt.figure(figsize=(10, 5))
#plt.plot(ellR, ellR * (ellR + 1) * clR)
plt.semilogy(ellR, clR)
#plt.plot(ell, ell * (ell + 1) * cl/2000)
plt.xlabel("$\ell$")
plt.ylabel("$C_{\ell}$")
plt.title('R = 4 x halfMassRadius')
plt.grid()
#plt.xlim(0,17)

END

In [177]:
start = time.time()

#velocities = readsnap(infile, 'vel', 'dm')
end = time.time()
print("Snapshot readed in %f s." %(end-start))
Returning DM    Positions
Snapshot readed in 0.263317 s.
In [188]:
from mpl_toolkits.mplot3d import * #3D-s ábrák alcsomagja
from ipywidgets import *  #interaktivitáshoz szükséges függvények
In [195]:
plt.plot(stack,'.')
Out[195]:
[<matplotlib.lines.Line2D at 0x7f82adb576a0>]
In [255]:
ss = hp.sphtfunc.smoothing(stack,0.4)
xyzDist = hp.pix2vec(NSIDE, range(len(ss))) * (ss-0.95*ss.mean())
Sigma is 583.950655 arcmin (0.169864 rad) 
-> fwhm is 1375.098708 arcmin
Sigma is 0.000000 arcmin (0.000000 rad) 
-> fwhm is 0.000000 arcmin
In [256]:
from plotly import *
from plotly.offline import *
from plotly.graph_objs import *
init_notebook_mode()
trace = Scatter3d(x=xyzDist[0,:], y=xyzDist[1,:], z=xyzDist[2,:], mode='markers', 
        marker=dict(
        size=1,
        colorscale='Viridis',   # choose a colorscale
        opacity=0.8
        )
                 ) # Adatok csoportosítása trace-be
adatok = [trace]
layout3d=Layout(title='3d')
fig_3D = Figure(data=adatok,layout=layout3d) # ábra objektum létrehozása
iplot(fig_3D) # ábra megjelenítése
In [262]:
plt.figure(figsize=(10,10))
plt.plot(xyzDist[0,:],xyzDist[1,:],'.')
Out[262]:
[<matplotlib.lines.Line2D at 0x7f82ade469b0>]
In [ ]: